Single landmark feedback-based time optimal navigation for a differential drive robot

In this paper, we propose a feedback-based control approach to execute the time optimal motion trajectories for a differential drive robot. These trajectories are composed of straight lines and rotations in place. We show that the evolution of the position of a single landmark over time, in a local...

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Bibliographic Details
Published in:Journal of the Franklin Institute 2021-06, Vol.358 (9), p.4761-4792
Main Authors: Macias, Vladimir, Becerra, Israel, Martinez, Edgar, Murrieta-Cid, Rafael, Becerrra, Hector M.
Format: Article
Language:English
Subjects:
Closed loop systems
Feedback
Feedback control
Feedback control systems
Navigation
Optimal control
Perturbation
Robot dynamics
Robotics
Robots
Servocontrol
Straight lines
Time optimal control
Tracking errors
Trajectory control
Trajectory optimization
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Summary:In this paper, we propose a feedback-based control approach to execute the time optimal motion trajectories for a differential drive robot. These trajectories are composed of straight lines and rotations in place. We show that the evolution of the position of a single landmark over time, in a local reference frame, makes it possible to track a prescribed time-optimal robot’s trajectory, based on feedback of the landmark’s position. We also show that the closed-loop system is an exponentially stable one with a nonvanishing perturbation, and that globally uniformly ultimately boundedness of the tracking errors can be achieved. The two main results of this work are: 1) Our approach leverages visual servo control type of methods with tools from optimal control for executing time-optimal trajectories in the state space based on feedback information. 2) The approach is able to work with the minimum number of landmarks–only one–this represents a necessary and sufficientcondition for landmark-based navigation. Experiments in a physical robot, a nonholonomic differential drive system equipped with an omnidirectional laser sensor, are shown, which validate the proposed theoretical modelling.
ISSN:0016-0032
1879-2693
0016-0032
DOI:10.1016/j.jfranklin.2021.04.015